What do the numbers in this CNN architecture stand for?
This number refers to the number of kernels (or feature maps) that are convolved with the input. So, for example, in the first convolutional layer, $64$ $3 \times 3$ kernels are convolved with the image.

The ResNet presented in Deep Residual Learning for Image Recognition is used for image classification. Furthermore, note that your diagram already contains a fully connected layer at the end.